The present invention relates to recording apparatuses, such as a digital copier and a laser beam printer, in which an image is written using a light beam. More specifically, the invention relates to a recording apparatus which employs a light source unit having a plurality of light sources, such as a multi-beam semiconductor laser array, and which scans a scanning surface with a plurality of light beams simultaneously to record information.
In a laser beam printer, for example, a laser beam emitted from a semiconductor laser is incident on a rotary multi-face mirror (i.e., polygon scanner), and a beam reflected from the polygon scanner is then incident on a charged surface of a photoreceptor which is moving at a constant speed. The rotation of the polygon scanner causes the laser beam to move in a direction perpendicular to the moving direction of the photoreceptor. Since the laser beam is modulated in accordance with an image to be output, a corresponding electrostatic latent image is formed on the photoreceptor surface. The electrostatic latent image is developed to become a visible toner image.
Such a laser beam printer is required to have a narrow interval of adjacent scanning lines, to provide high-resolution output images. Further, the scanning speed should be sufficiently high to produce images at a high speed. In attaining the high resolution and the high output speed, the most serious problem is a limited rotational speed of the polygon scanner.
To solve this problem, the "multi-beam scanning" has been proposed in which a scanning surface is scanned with a plurality of laser beams simultaneously. In this scanning method, a plurality of laser beam spots should be placed sufficiently close to each other on the scanning surface in a direction (hereinafter called "sub-scanning direction") perpendicular to a scanning direction (hereinafter called "main scanning direction") of the polygon scanner. To this end, various efforts have been made to manufacture a plurality of semiconductor lasers arranged sufficiently close to each other. Semiconductor laser arrays having laser intervals as small as 10 .mu.m have already been produced experimentally. (For example, refer to Japanese Patent Application Unexamined Publication No. Hei. 2-39583, and R. L. Thornton et al., "Properties of closely spaced independently addressable lasers fabricated by impurity-induced disordering", Appl. Phys. Lett., 56(17), pp. 1623-1625, 1990.)
However, even with a plurality of semiconductor lasers arranged close to each other at intervals as small as 10 .mu.m, there still exists some gap in the sub-scanning direction, i.e, between adjacent scanning lines. To solve this problem, it has been proposed to eliminate such gaps in the sub-scanning direction by the interlaced scanning (Japanese Patent Application Examined Publication No. Hei. 1-45065, and K. Minoura et al., "A study on laser scanning systems using a monolithic arrayed laser diode", SPIE Vol. 1079, pp. 462-474, 1989). Further, the present assignee has developed a multi-beam scanning optical system in which such gaps are eliminated by interlaced scanning using an array of semiconductor lasers arranged at intervals of 10 .mu.m (Japanese Patent Application Unexamined Publication No. Hei. 3-248114).
FIG. 6 shows an example of the interlaced scanning, which uses two laser beams L.sub.1 and L.sub.2. In this figure, d.sub.x represents a laser beam spot diameter defined electrophotographically (hereinafter referred to as "electrophotographic spot diameter"). The electrophotographic spot diameter does not mean a diameter of a beam spot itself on a scanning surface A, but a diameter of a spot that appears after development of an electrostatic latent image formed by laser light exposure of the scanning surface A which is a charged photoreceptor. A center-to-center interval r.sub.3 between two spots B.sub.1 and B.sub.2 on the scanning surface A of the respective laser beams L.sub.1 and L.sub.2 is 3d.sub.x.
In the example of FIG. 6, sub-scanning of a distance 2d.sub.x is performed for each main scanning. The second scanning line is scanned with the laser beam L.sub.2 in the first main scanning. Then, in the second main scanning, the first scanning line and the fourth scanning lines are scanned with the laser beams L.sub.1 and L.sub.2, respectively. Thereafter, the scanning operation is continued in this manner so as to avoid formation of any gaps in the sub-scanning direction. That is, although a gap is formed in certain main scanning, it is scanned in the next scanning, so that no gaps remain after completion of the scanning operation.
In the interlaced scanning, it is required that the following three conditions be satisfied to avoid generation of doubly scanned lines and non-scanned lines.
1) If there exist n laser beams, the sub-scanning distance for each main scanning should be nd.sub.x.
2) The interval r.sub.3 between the two laser beams on the scanning surface should be an integer multiple of the electrophotographic spot diameter.
3) A scanning line which has already been scanned in certain main scanning should not be scanned in another main scanning.
As is disclosed in the above paper by K. Minoura et al., the third condition is satisfied when following equation (1) holds: EQU p=.beta.r/(mn+1) (1)
where n represents the number of laser light sources, r the interval of the laser light sources, .beta. the lateral magnification in the sub-scanning direction of an image forming optical system, p the scanning pitch, and m an integer not less than zero. If m=0, equation (1) represents the non-interlaced case in which adjacent spots are closely arranged in the sub-scanning direction. It is noted that in the above paper by K. Minoura et al. characters M and p.sub.0 are used instead of M and r in equation (1), respectively.
The scanning pitch p, i.e., a minimum interval between scanning lines, is also shown in FIG. 6. In order to perform a scanning operation by a single laser beam without leaving gaps on the scanning surface, it is generally required that the scanning pitch p be equal to the electrophotographic spot diameter d.sub.2.
The interval .beta.r of the beam spots of the multi-beam laser array is expressed as .beta.r=Ip, where I is a positive integer and is called "interlacing period".
In general, the spot diameter of a laser beam is defined by a diameter having the two ends where the light amplitude is 1/e (1/e.sup.2 in terms of power) of that at the center. The spot diameter according to this definition is called "optical spot diameter" and represented by d.sub.0.
FIG. 7 shows a relationship between the optical spot diameter d.sub.0 and the electrophotographic spot diameter d.sub.x, in which the light intensity on the axis of a laser beam is normalized to 1. A ratio k of the optical spot diameter d.sub.0 to the electrophotographic spot diameter d.sub.x, i.e., k=d.sub.0 /d.sub.x, is called "spot diameter correction coefficient". The actual value of k varies depending on the electrophotographic process employed. In the inversion development process, in which toner is stuck to portions exposed to light, it is desirable that k be in the range of 1.4 to 1.6. On the other hand, in the case of the normal development process, in which toner is stuck to portions not exposed to light, it is desirable that k be in the range of 1.5 to 1.8 (T. Tanaka, "Study of Gradation Reproduction in Laser Xerography", 6th Conference of Chromatic Engineering, pp. 77-80, 1989).
In the above-described interlaced scanning, it may be conceivable that the interval of the spots formed on the scanning surface can be set as large as desired by properly selecting the integer m. However, practically, if the spot interval is too large, the scanning device is required to have extremely high mechanical accuracy. This is explained below.
Where a scanning surface is scanned by a single light beam as shown in FIG. 9, if it is required that an error of the scanning pitch p between spots B be within a limit .DELTA.p, an allowable error factor .delta..sub.0, i.e., a ratio of a sub-scanning speed error .DELTA.v to a sub-scanning speed v is expressed as: EQU .delta..sub.0 .DELTA.v/v=.DELTA.p/p.
In the case of FIG. 10, in which n=4 and m=1, an allowable error factor .delta..sub.4,1 is calculated as: .delta..sub.4,1 .DELTA.p/16p=.delta..sub.0 /16. Therefore, the required accuracy is higher than the case of FIG. 9 by more than one order. This tendency becomes more remarkable with increases of the number n of light sources and the integer m.
While the allowable error of the sub-scanning speed is described above, similar problems in connection with accuracy occur in the lateral magnification of the optical system and in the interval between the light sources.
Apparently, it is desirable, to solve the above problems, that the interval between the spots on the scanning surface be as small as possible. In equation (1) described above, the spot interval is smallest when m=0, but this is not an interlaced scanning case. Therefore, we should consider the case of m=1 in equation (1), which will provide the smallest spot interval among the interlaced scanning cases. When m=1, the interval .beta.r between the adjacent spots on the scanning surface is expressed as (n+1)p and increases with the number n of the light sources.
Considering the above, the allowable error factor .delta..sub.n,m for the number n of the light sources and the integer m has the following relationship: EQU .delta..sub.n,m .gtoreq..delta..sub.n,1 .delta..sub.0 /n.sup.2.(2)
This is schematically illustrated in FIG. 8. When m =1, since each spot interval is (n+1)p, the two most distant spots have an interval of (n.sub.2 -1)p. A last spot B of the first scanning should be adjacent, in the sub-scanning direction, to a head spot C of the n-th scanning.
Another problem arises when it is intended to expand the spot interval on the scanning surface. That is, in performing a plural times of scanning to scan the area between the two scanning lines of the adjacent beams, capacity of high-speed memories necessary for electrically controlling the interlaced scanning is increased with the number of lines to be skipped.